Effect of the Electromagnetic Environment on Single Charge Tunneling

For tunnel junctions with very small capacitance one expects that charging effects play an important role. They may manifest themselves for example in the Coulomb gap appearing in the current-voltage characteristic. On the other hand, thermal and quantum fluctuations tend to suppress charging effects. At sufficiently low temperatures one may neglect thermal fluctuations and it is then important to study the influence of the circuit connected to the junction. It is shown that for a single tunnel junction a high impedance environment is crucial for the observability of a Coulomb gap in the I-V characteristic. For systems consisting of two or more tunnel junctions the existence of a quantized island charge always ensures the existence of a Coulomb gap and the influence of the environment becomes less important.